Error estimate in the generalized Szegö theorem

Ingham Tauberian Theorem with an Estimate for the Error Term

We estimate the error term in the Ingham Tauberian theorem. This estimation of the error term is accomplished by considering an elementary proof of a weak form of Wiener's general Tauberian theorem and by using a zero-free region for the Riemann zeta function. 1. Introduction. As an important application of his general Tauberian theorem (GTT), in 1932, Wiener [6] gave a new proof of the prime n...

Generalized holomorphic Szegö kernel in 3D spheroids

Monogenic orthogonal polynomials over 3D prolate spheroids were previously introduced and shown to have some remarkable properties. In particular, the underlying functions take values in the quaternions (identified with R), and are generally assumed to be nullsolutions of the well known Moisil-Théodoresco system. In this paper, we show that these polynomial functions play an important role in d...

GENERALIZATION OF TITCHMARSH'S THEOREM FOR THE GENERALIZED FOURIER-BESSEL TRANSFORM

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.

A Fixed Point Theorem in Generalized D-metric Spaces

GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES

The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.